In the past, methods for analyzing magnetic field sources using a super computer were based upon output from plural flux meters and Monte Carlo analysis; methods applied to adaptive noise cancelers; methods which incorporate an impulse response estimating apparatus; and methods which determine threshold values, coupling coefficients, and the like, of neuron devices which constitute a neural network based upon physical formulae of a system so as to omit learning time required for these neuron devices (refer to Japanese Patent Laid Open Tokukaihei 5-94543), are proposed as physical quantity analyzing methods. Further, a finite element method is also proposed as physical quantity analyzing method.
The method for analyzing magnetic field sources typically involves the following processing:
a) Scatter m-number current elements using random numbers within a search space which is searched by plural flux meters; PA1 b) calculate a total estimated error (a sum of all estimated errors) by an estimated error calculating process; PA1 c) Repeat the following processing d) to g); PA1 d) Select a current element k arbitrarily, and evacuating parameters of corresponding current element and the total estimated error; PA1 e) Vary parameters of the current element k by extremely small quantities using random numbers; PA1 f) Calculate a total estimated error by the estimated error calculating process; PA1 g) Compare the evacuated total estimated error and the total estimated error calculated in f), and restore the information which are evacuated at d) when the evacuated total estimated error is smaller than the total estimated error calculated in f). PA1 provisionally determining a physical quantity u.sub.i of each physical source, PA1 calculating a physical quantity O.sub.j by carrying out an operation of equation (1) based upon the provisionally determined physical quantity u.sub.i, PA1 determining and employing a value which minimizes a sum of squares of differences as a physical quantity of a physical source based upon a difference and corresponding proportional constants, the difference being a difference between the calculated physical quantity O.sub.j and corresponding known physical quantity S.sub.j, PA1 repeating the calculation of the difference and the employing of the physical quantities u.sub.i for each of the physical sources, PA1 continuing to repeat the calculations of the differences and the determination of the physical quantities u.sub.i for each physical source until the sum of the squares of the differences which is obtained by the repetition of the processing becomes smaller than a predetermined threshold value, and PA1 employing the physical quantities u.sub.i of each of the physical sources which are finally obtained. PA1 predetermining constants each of which represents a physical characteristic provided at each predetermined position by a physical source having a unit quantity corresponding to the individual physical source, PA1 calculating a difference between a measured physical quantity at each predetermined position and a sum of products of each physical quantity and corresponding constant, PA1 determining and employing a value which minimize a sum of squares of differences as a new physical quantity based upon the calculated differences and each constant, PA1 repeating the calculation of the differences and the employing of the physical quantities u.sub.i for each physical source, PA1 continuing to repeat the calculation of the difference and the employing of the physical quantities u.sub.i for each physical source until the sum of the squares of the differences which is obtained by the repetition of the process becomes smaller than a predetermined threshold value, and PA1 employing the physical quantities u.sub.i of each physical source which are finally obtained. PA1 (1) predetermining constants .alpha..sub.ij each of which represents a measurable physical characteristic provided at each predetermined position by a physical source having a unit quantity corresponding to the individual physical source, PA1 (2) provisionally determining a physical quantity u.sub.i for each physical source, PA1 (3) calculating a physical quantity O.sub.j which is expected to be provided at the measurement point j by carrying out the operation of the equation: ##EQU3## (4) calculating a difference S.sub.j -O.sub.j between an actual measurement value S.sub.j at the measurement point j and the physical quantity O.sub.j, PA1 (5) obtaining a physical quantity u.sub.i as a provisional solution by carrying out the equation: ##EQU4## (6) carrying out the steps (3) to (5) for each physical source, (7) continuing to repeat the process of steps (3) to (5) until a sum of the squares of the differences S.sub.j -O.sub.j is less than a predetermined threshold value, and employing the physical quantity of each physical source which is finally obtained as a result. PA1 (1) predetermining constants .alpha..sub.ij each of which represents a magnetic field generated at each predetermined position by a magnetic field source having a unit quantity corresponding to an individual magnetic field source, PA1 (2) provisionally determining a physical quantity u.sub.i for each magnetic field source whose position corresponds to a lattice point k (k=1, 2, ..., p) within the object body, PA1 (3) calculating a magnetic field O.sub.j which is expected to be generated at a measurement point j by carrying out the operation of the equation: EQU O.sub.j =.SIGMA..alpha..sub.ij .multidot.u.sub.i ( 1) PA1 (4) calculating a difference S.sub.j -O.sub.j between an actual measurement value S.sub.j of a magnetic field at the measurement point j and the magnetic field O.sub.j, PA1 (5) obtaining a physical quantity u.sub.i as a provisional solution by carrying out operation of the equation: ##EQU5## (6) performing steps (3) to (5) for all magnetic field sources, (7) continuing to repeat the process of steps (3) to (5) until the sum of the squares of the differences S.sub.j -O.sub.j is less than a predetermined threshold value. PA1 measuring a physical quantity u.sub.i at a predetermined position which is proximal to at least one physical source, PA1 provisionally determining degrees each of which represents an influence at the predetermined position by the physical source, PA1 calculating a difference between a measured physical quantity u.sub.i at each predetermined position and a sum of products of each measured physical quantity and corresponding degree, PA1 determining and employing a value which minimizes a sum of squares of differences for each new physical quantity based upon the calculated differences and each physical quantity measurement value, PA1 repeating the calculation of difference and the determination and employment of physical quantities u.sub.i for each physical source, and PA1 continuing to repeat the calculation of the difference and the employing of the physical quantities u.sub.i for each physical source until a sum of the squares of the differences which is obtained by the repetition of the processings becomes smaller than a predetermined threshold value, and thereafter employing the physical quantities of each physical source which are finally obtained at the predetermined positions. PA1 measuring a physical aspect of an active physical source, PA1 provisionally determining a physical aspect of a passive physical source, PA1 calculating a difference between a measured physical quantity at a predetermined position and a sum of products of each measured physical quantity of the active physical source and the physical quantity of the passive physical source, PA1 determining and employing a value which minimizes a sum of squares of differences for each new physical quantity based upon the calculated differences and based upon each physical quantity measurement value of each active physical source, PA1 repeating the calculation of the difference and the determination and employment of the physical quantities for each physical source, PA1 continuing to repeat the calculation of the difference and the determination and employment of the physical quantities for each physical source until the sum of the squares of the differences which is obtained by the repetition of the processings becomes smaller than a predetermined threshold value, and PA1 employing the physical quantities of each physical source which are finally obtained as physical quantities of the passive physical source. PA1 obtaining proportion constants which are determined for a particular region, PA1 provisionally determining physical quantities at plural predetermined positions, PA1 calculating a difference between a known physical quantity which is given within the region at each predetermined position and a sum of products of each physical quantity and corresponding proportion constant, PA1 determining and employing a value which minimizes a sum of squares of differences for each new physical quantity based upon the calculated differences and each physical quantity measurement value of each active physical source, PA1 repeating the calculation of the difference and the determination and employment of the physical quantities for each physical source, PA1 continuing to repeat the calculating of the differences and the determination and employment of the physical quantities for each physical source until a sum of the squares of the differences which is obtained by the repetition of the processing becomes smaller than a predetermined threshold value, and PA1 employing the physical quantity which is finally obtained as physical quantity for the predetermined position. PA1 (1) obtaining (N.sub.x -1).times.N.sub.y .times.N.sub.z number of G.sub.x [k.sub.x, k.sub.y, k.sub.z ], PA1 (2) obtaining N.sub.x .times.(N.sub.y -1).times.N.sub.z number of G.sub.y [k.sub.x, k.sub.y, k.sub.z ], PA1 (3) obtaining N.sub.x .times.N.sub.y .times.(N.sub.z -1) number of G.sub.z [k.sub.x, k.sub.y, k.sub.z ], PA1 (4) obtaining N.sub.x .times.N.sub.y .times.N.sub.z number of G.sub.N [k.sub.x, k.sub.y, k.sub.z ], PA1 (5) obtaining N.sub.x .times.N.sub.y .times.N.sub.z number of .beta.[k.sub.x, k.sub.y, k.sub.z ] based upon the equation: ##EQU9## (6) calculating correction values .DELTA.u of the potentials u[k.sub.x, k.sub.y, k.sub.z ] based upon ##EQU10## (7) correcting the potential u[k.sub.x, k.sub.y, k.sub.z ] by adding the calculated correction value .DELTA.u, PA1 (8) repeating the process of steps (6) and (7) for 1 to N.sub.z for k.sub.z, PA1 (9) repeating the process of steps (6) to (8) for 1 to N.sub.y for k.sub.y, PA1 (10) repeating the process of steps (6) to (9) for 1 to N.sub.x for k.sub.x, and PA1 (11) repeating the process of steps (6) to (10) until an estimated error becomes smaller than a predetermined threshold value, and employing the potentials which are finally obtained as the analysis result. PA1 (1) provisionally determining a current which flows into one lattice point and flows out of another lattice point as a physical source for analysis, PA1 (2) calculating an estimated value of a potential on a surface of the region selected for analysis by multiplying the provisionally determined physical quantity and a proportion constant, PA1 (3) calculating a correction value for a physical quantity based upon a difference between the measured potential and the estimated value of the potential, PA1 (4) correcting the physical quantity based upon the calculated correction value, PA1 (5) repeating the process of steps (2) to (4) for all physical quantities, and PA1 (6) repeating the process of steps (2) to (5) until an estimated error becomes smaller than a predetermined threshold value, and employing the physical quantities which are finally obtained. PA1 (1) selecting a first and a second physical quantities from among a plurality of physical quantities, PA1 (2) calculating a correction value for each selected physical quantity based upon the formula; ##EQU11## (3) correcting corresponding physical quantities based upon the calculation for each correction value, PA1 (4) correcting the first physical quantity by carrying out the process of steps (2) and (3), PA1 (5) correcting the second physical quantity by carrying out the process of steps (2) and (3), PA1 (6) correcting the first physical quantity again by carrying out the process of steps (2) and (3), PA1 (7) calculating a correction value for correcting the second physical quantity again, by carrying out the process of step (2), PA1 (8) calculating a correction value for the first physical quantity by dividing a product of the correction values which are obtained in steps (6) and (7) by a difference between the correction value obtained in the step (4) and the correction value obtained in the step (6), PA1 (9) calculating a correction value for the second physical quantity by dividing a product of the correction values which are obtained in steps (5) and (7) by a difference between the correction value obtained in step (4) and the correction value obtained in step (5), PA1 (10) correcting the first physical quantity based upon the correction values obtained in step (6), and correcting the second physical quantity based upon the correction values obtained in step (9), PA1 (11) selecting two additional physical quantities and carrying out the process of steps (4) to (10), and PA1 (12) repeating the process of steps (4) through (11) until an estimated error becomes smaller than a predetermined threshold value, and employing the physical quantities which are finally obtained. PA1 calculating estimated errors: EQU D[k.sub.x, k.sub.y, k.sub.z ]=(S[k.sub.x, k.sub.y, k.sub.z ]-O[k.sub.x, k.sub.y, k.sub.z ]), EQU D[k.sub.x -1, k.sub.y, k.sub.z ]-(S[k.sub.x -1, k.sub.y, k.sub.z ]-O[k.sub.x -1, k.sub.y, k.sub.z ]), EQU D[k.sub.x +1, k.sub.y, k.sub.z ]=(S[k.sub.x +1, k.sub.y, k.sub.z ]-O[k.sub.x +1, k.sub.y, k.sub.z ]), EQU D[k.sub.x, k.sub.y -1, k.sub.z ]=(S[k.sub.x, k.sub.y -1, k.sub.z ]-O[k.sub.x, k.sub.y -1, k.sub.z ]), EQU D[k.sub.x, k.sub.y +1, k.sub.z ]=(S[k.sub.x, k.sub.y +1, k.sub.z ]-O[k.sub.x, k.sub.y +1, k.sub.z ]), EQU D[k.sub.x, k.sub.y, k.sub.z -1]=(S[k.sub.x, k.sub.y, k.sub.z -1]-O[k.sub.x, k.sub.y, k.sub.z -1]), EQU D[k.sub.x, k.sub.y, k.sub.z +1]=(S[k.sub.x, k.sub.y, k.sub.z +1]-O[k.sub.x, k.sub.y, k.sub.z +1]), PA1 and PA1 correcting the estimated errors based upon formulae: EQU D[k.sub.x, k.sub.y, k.sub.z ].rarw.(D[k.sub.x, k.sub.y, k.sub.z ]+G.sub.N [k.sub.x, k.sub.y, k.sub.z]).DELTA.u EQU D[k.sub.x -1, k.sub.y, k.sub.z ].rarw.(D[k.sub.x -1, k.sub.y, k.sub.z ]+G.sub.x [k.sub.x -1, k.sub.y, k.sub.z ]).DELTA.u EQU D[k.sub.x +1, k.sub.y, k.sub.z ].rarw.(D[k.sub.x +1, k.sub.y, k.sub.z ]+G.sub.x [k.sub.x, k.sub.y, k.sub.z ]).DELTA.u EQU D[k.sub.x, k.sub.y -1, k.sub.z ].rarw.(D[k.sub.x, k.sub.y -1, k.sub.z ]+G.sub.y [k.sub.x, k.sub.y -1, k.sub.z ]).DELTA.u EQU D[k.sub.x, k.sub.y +1, k.sub.z ].rarw.(D[k.sub.x, k.sub.y +1, k.sub.z ]+G.sub.y [k.sub.x, k.sub.y, k.sub.z ]).DELTA.u EQU D[k.sub.x, k.sub.y, k.sub.z -1].rarw.(D[k.sub.x, k.sub.y, k.sub.z -1]+G.sub.z [k.sub.x, k.sub.y k.sub.z -1]).DELTA.u EQU D[k.sub.x, k.sub.y, k.sub.z -1].rarw.(D[k.sub.x, k.sub.y, k.sub.z +1]+G.sub.z [k.sub.x, k.sub.y, k.sub.z ]).DELTA.u (9), PA1 wherein D[k.sub.x, k.sub.y, k.sub.z ], D[k.sub.x -1, k.sub.y, k.sub.z ], D[k.sub.x +1, k.sub.y, k.sub.z ], D[k.sub.x, k.sub.y -1, k.sub.z ], D[k.sub.x, k.sub.y +1, k.sub.z ], D[k.sub.x, k.sub.y, k.sub.z -1], D[k.sub.x, k.sub.y, k.sub.z +1] are employed instead of EQU (S[k.sub.x, k.sub.y, k.sub.z ]-O[k.sub.x, k.sub.y, k.sub.z ]), EQU (S[k.sub.x -1, k.sub.y, k.sub.z ]-O[k.sub.x -1, k.sub.y, k.sub.z ]), EQU (S[k.sub.x +1, k.sub.y, k.sub.z ]-O[k.sub.x +1, k.sub.y, k.sub.z ]), EQU (S[k.sub.x, k.sub.y -1, k.sub.z ]-O[k.sub.x, k.sub.y -1, k.sub.z ]), EQU (S[k.sub.x, k.sub.y +1, k.sub.z ]-O[k.sub.x, k.sub.y +1, k.sub.z ]), EQU (S[k.sub.x, k.sub.y, k.sub.z -1]-O[k.sub.x, k.sub.y, k.sub.z -1]), EQU (S[k.sub.x, k.sub.y, k.sub.z +1]-O[k.sub.x, k.sub.y, k.sub.z +1]) PA1 in the formula: ##EQU12## PA1 physical quantity provisional determining means for provisionally determining a physical quantity u.sub.i of each physical source, PA1 physical quantity calculating means for calculating a physical quantity O.sub.j by carrying out an operation of equation (1) based upon each physical quantity u.sub.i determined, and employing a value which minimizes a sum of squares of differences based upon the differences and corresponding proportional constants, which difference is a difference between the calculated physical quantity O.sub.j and a corresponding known physical quantity S.sub.j, PA1 first repetition controlling means for repeating the calculation of the difference and the employing of the physical quantities u.sub.i for each physical source, PA1 second repetition controlling means for continuing the repetition of the calculation of the difference by the first repetition controlling means and the employing of the physical quantities u.sub.i for each physical source until the sum of the squares of the differences which is obtained by the repetition of the processing becomes smaller than a predetermined threshold value, and PA1 physical quantity employment means for employing the physical quantities u.sub.i of each physical source which are finally obtained as physical quantities u.sub.i of each physical source. PA1 constant determining means for predetermining constants each of which represents a physical field generated at each predetermined position by a physical source having a unit quantity corresponding to the individual physical source, PA1 difference calculating means for calculating a difference between a measured physical quantity at each predetermined position and a sum of products of each physical quantity and corresponding constant, PA1 physical quantity correcting means for employing a value which minimizes a sum of squares of differences for each new physical quantity based upon the calculated differences and each constant, PA1 first repetition controlling means for repetitively operating the difference calculating means and the physical quantity correcting means for each physical source, and PA1 physical quantity employment means for repetitively operating the repetitive operations of the difference calculating means and the physical quantity correcting means for each physical source by the first repetition controlling means, and for employing the physical quantities of each physical source which are finally obtained as physical quantities of each physical source. PA1 (1) means for predetermining constants .alpha..sub.ij each of which represents a physical field generated at each predetermined position by a physical source, .alpha..sub.ij having a unit quantity corresponding to the individual physical source, PA1 (2) means for provisionally determining the physical quantity u.sub.i of each physical source, PA1 (3) means for calculating a physical quantity O.sub.j which may be generated at the measurement point j by carrying out the operation of the equation: ##EQU14## (4) means for calculating a differences S.sub.j -O.sub.j between an actual measurement value S.sub.j at the measurement point j and the physical quantity O.sub.j, PA1 (5) means for obtaining a physical quantity u.sub.i as a provisional solution by carrying out operation of the equation: ##EQU15## (6) means for carrying out the operation of each of the means (3) to (5) for each physical source i, PA1 (7) means for continuing the repeating operation of the processing of each of the means (3) to (5) until the sum of the squares of the differences S.sub.j -O.sub.j is less than a predetermined threshold value, and PA1 (8) means for employing the physical quantity u.sub.i of each physical source as the physical quantity u.sub.i of each physical source which is finally obtained as an analysis result. PA1 (1) means for predetermining constants .alpha..sub.ij each of which represents a magnetic field generated at a predetermined position by a magnetic field source having a unit quantity corresponding to the individual magnetic field source, PA1 (2) means for provisionally determining physical quantity u.sub.i for each magnetic field source which is positioned at a lattice point k (k-1, 2, . . . , p) within the object, PA1 (3) means for calculating a magnetic field O.sub.j which is generated at the measurement point j by carrying out the operation of the equation: ##EQU16## (4) means for calculating a differences S.sub.j -O.sub.j between an actual measurement value S.sub.j of the magnetic field at the measurement point j and the magnetic field O.sub.j, PA1 (5) means for obtaining a physical quantity u.sub.i as a provisional solution by carrying out operation of the equation: ##EQU17## (6) means for carrying out the processing by each of the means (3) to (5) for each magnetic field source. PA1 (7) means for repeating the processing by each of the means (3) to (5) until the sum of the squares of the differences S.sub.j -O.sub.j is less than a predetermined threshold value, and PA1 (8) means for employing the physical quantity which is finally obtained as analysis result. PA1 physical quantity measuring means for measuring a physical quantity at a predetermined position which is proximal to at least one physical source, PA1 provisional degree determining means for provisionally determining degrees each of which represents an influence at the predetermined position by the physical source, PA1 difference calculating means for calculating a difference between a measured physical quantity at each predetermined position and a sum of products of each measured physical quantity and corresponding degree, PA1 physical quantity correcting means for employing a value which minimizes a sum of squares of differences for each new physical quantity based upon the calculated differences and each physical quantity measurement value, PA1 first repetition controlling means for repetitively operating the difference calculating means and the physical quantity correcting means for each physical source, and PA1 physical quantity employment means for continuing the repetition of the difference calculating means and the physical quantity correcting means by the first repetition controlling means for each physical source until the sum of the squares of the differences which is obtained by the repetition of the processing becomes smaller than a predetermined threshold value, and for employing the physical quantities of each physical source which are finally obtained as physical quantities which are observed at the predetermined positions. PA1 physical quantity measuring means for measuring a physical quantity of the active physical source, PA1 provisional physical quantity determining means for provisionally determining a physical quantity of the passive physical source, PA1 difference calculating means for calculating a difference between a measured physical quantity at a predetermined position and a sum of products of each measured physical quantity of the active physical source and the physical quantity of the passive physical source, PA1 physical quantity correcting means for employing a value which minimizes a sum of squares of differences for each new physical quantity based upon the calculated differences and each physical quantity measurement value of each active physical source, PA1 first repetition controlling means for repetitively operating the difference calculating means and the physical quantity correcting means for each physical source, and PA1 physical quantity employment means for continuing the repetition of the difference calculating means and the physical quantity correcting means by the first repetition controlling means for each physical source until a sum of the squares of the differences which is obtained by the repetition of the processing becomes smaller than a predetermined threshold value, and for employing the physical quantities of each physical source which are finally obtained as physical quantities of the passive physical source. PA1 proportion constant holding means for obtaining and holding the proportion constants which are determined based upon a region, PA1 provisional physical quantity determining means for provisionally determining physical quantities at plural predetermined positions which are predetermined, PA1 difference calculating means for calculating a difference between a known physical quantity which is given within the region at each predetermined position, and a sum of products of each physical quantity and corresponding proportion constant, PA1 physical quantity renewing means for employing a value which minimizes a sum of squares of differences for each new physical quantity based upon the calculated differences and each physical quantity measurement value of each active physical source, PA1 first repetition controlling means for repeating the calculation of the difference by the difference calculating means and the employment of the physical quantities by the physical quantity renewing means for each physical source, and PA1 physical quantity employment means for continuing the repetition of the calculating of the difference by the difference calculating means and the employing of the physical quantities for each physical source until a sum of the squares of the differences, which is obtained by the repetition of the processing, becomes smaller than a predetermined threshold value, and for employing the physical quantity which is finally obtained as physical quantity at the predetermined position. PA1 (1) means for obtaining (N.sub.x -1).times.N.sub.y .times.N.sub.z number of G.sub.x [k.sub.x, k.sub.y, k.sub.z ], PA1 (2) means for obtaining N.sub.x .times.(N.sub.y -1).times.N.sub.z number of G.sub.y [k.sub.x, k.sub.y, k.sub.z ], PA1 (3) means for obtaining N.sub.x .times.N.sub.y .times.(N.sub.z -1) number of G.sub.z [k.sub.x, k.sub.y, k.sub.z ], PA1 (4) means for obtaining N.sub.x .times.N.sub.y .times.N.sub.z number of G.sub.N [k.sub.x, k.sub.y, k.sub.z ], PA1 (5) means for obtaining N.sub.x .times.N.sub.y .times.N.sub.z number of .beta.[k.sub.x, k.sub.y, k.sub.z ] based upon the equation: ##EQU21## (6) means for calculating correction values .DELTA.u of the potentials u[k.sub.x, k.sub.y, k.sub.z ] based upon the formula: ##EQU22## (7) means for correcting the potential u[k.sub.x, k.sub.y, k.sub.z ] by adding the calculated correction value .DELTA.u, PA1 (8) means for repeating the process of the means (6) and (7) for 1 to N.sub.z for k.sub.z, PA1 (9) means for repeating the process of the means (6) to (8) for 1 to N.sub.y for k.sup.y, PA1 (10) means for repeating the process of the means (6) to (9) for 1 to N.sub.x for k.sub.x, and PA1 (11) means for repeating the process of the means (6) to (10) until an estimated error becomes smaller than a predetermined threshold value, and for employing the potentials which are finally obtained. PA1 (1) means for provisionally determining a current flows into a lattice point and flows out from another lattice point for a physical source subject to analysis, PA1 (2) means for calculating an estimated value of a potential on a surface of the region subject to analysis by multiplying the provisionally determined physical quantity and a proportion constant, PA1 (3) means for calculating a correction value for a physical quantity based upon a difference between the measured potential and the estimated value of the potential, PA1 (4) means for correcting the physical quantity based upon the calculated correction value, PA1 (5) means for repetitively operating each of the means (2) to (4) for each physical quantity, and PA1 (6) means for iteratively operating each of the means (2) to (5) until an estimated error becomes smaller than a predetermined threshold value, and for employing the physical quantities which are finally obtained as a analysis result. PA1 (1) means for selecting two physical quantities from among plural physical quantities, PA1 (2) means for calculating a correction value of each selected physical quantity based upon the formula: ##EQU23## (3) means for correcting a corresponding physical quantity based upon each calculated correction value, PA1 (4) means for correcting a first physical quantity by operating each of means (2) and (3), PA1 (5) means for correcting a second physical quantity by operating each of means (2) and (3), PA1 (6) means for correcting the first physical quantity again by operating each of means (2) and (3), PA1 (7) means for calculating a correction value for correcting the second physical quantity again, by operating the means (2), PA1 (8) means for calculating a correction value for the first physical quantity by dividing a product of correction values which are obtained by operating each of means (6) and (7) by a difference between a correction value which is obtained by operating the means (4) and the correction value obtained by means (6), PA1 (9) means for calculating a correction value for the second physical quantity by dividing a product of correction values which are obtained by operating each of means (5) and (7) by a difference between a correction value which is obtained by operating the means (4) and the correction value which is obtained by operating the means (6), PA1 (10) means for correcting the physical quantities based upon a correction value which is obtained by operating each of means (8) and (9), PA1 (11) means for selecting two other physical quantities and for operating each of means (4) to (10), and PA1 (12) means for iteratively operating each of means (4) to (11) until an estimated error becomes smaller than a predetermined threshold value, and for employing the physical quantities which are finally obtained. PA1 means for calculating the estimated errors of EQU D[k.sub.x, k.sub.y, k.sub.z ]=(S[k.sub.x, k.sub.y, k.sub.z ]-O[k.sub.x, k.sub.y, k.sub.z ]), EQU D[k.sub.x -1, k.sub.y, k.sub.z ]=(S[k.sub.x -1, k.sub.y, k.sub.z ]-O[k.sub.x -1, k.sub.y, k.sub.z ]), EQU D[k.sub.x +1, k.sub.y, k.sub.z ]=(S[k.sub.x +1, k.sub.y, k.sub.z ]-O[k.sub.x +1, k.sub.y, k.sub.z ]), EQU D[k.sub.x, k.sub.y -1, k.sub.z ]=(S[k.sub.x, k.sub.y -1, k.sub.z ]-O[k.sub.x, k.sub.y -1, k.sub.z ]), EQU D[k.sub.x, k.sub.y +1, k.sub.z ]=(S[k.sub.x, k.sub.y +1, k.sub.z ]-O[k.sub.x, k.sub.y +1, k.sub.z ]), EQU D[k.sub.x, k.sub.y, k.sub.z -1]=(S[k.sub.x, k.sub.y, k.sub.z -1]-O[k.sub.x, k.sub.y, k.sub.z -1]), EQU D[k.sub.x, k.sub.y, k.sub.z +1]=(S[k.sub.x, k.sub.y, k.sub.z +1]-O[k.sub.x, k.sub.y, k.sub.z +1]) PA1 and PA1 means for correcting the estimated errors based upon the formulae EQU D[k.sub.x, k.sub.y, k.sub.z ].rarw.(D[k.sub.x, k.sub.y, k.sub.z ]+G.sub.N [k.sub.x, k.sub.y, k.sub.z ]).DELTA.u EQU D[k.sub.x -1, k.sub.y, k.sub.z ].rarw.(D[k.sub.x -1, k.sub.y, k.sub.z ]+G.sub.x [k.sub.x -1, k.sub.y, k.sub.z ]).DELTA.u EQU D[k.sub.x +1, k.sub.y, k.sub.z ].rarw.(D[k.sub.x +1, k.sub.y, k.sub.z ]+G.sub.x [k.sub.x, k.sub.y, k.sub.z ]).DELTA.u EQU D[k.sub.x, k.sub.y -1, k.sub.z ].rarw.(D[k.sub.x, k.sub.y -1, k.sub.z ]+G.sub.y [k.sub.x, k.sub.y -1, k.sub.z ]).DELTA.u EQU D[k.sub.x, k.sub.y +1, k.sub.z ].rarw.(D[k.sub.x, k.sub.y +1, k.sub.z ]+G.sub.y [k.sub.x, k.sub.y, k.sub.z ]).DELTA.u EQU D[k.sub.x, k.sub.y, k.sub.z -1].rarw.(D[k.sub.x, k.sub.y, k.sub.z -1+G.sub.y [k.sub.x, k.sub.y, k.sub.z -1]).DELTA.u EQU D[k.sub.x, k.sub.y, k.sub.z +1].rarw.(D[k.sub.x, k.sub.y, k.sub.z +1]+G.sub.y [k.sub.x, k.sub.y, k.sub.z ]).DELTA.u (9) PA1 wherein D[k.sub.x, k.sub.y, k.sub.z ], D[k.sub.x -1, k.sub.y, k.sub.z ], D[k.sub.x +1, k.sub.y, k.sub.z ], D[k.sub.x, k.sub.y -1, k.sub.z ], D[k.sub.x, k.sub.y +1, k.sub.z ], D[k.sub.x, k.sub.y, k.sub.z -1], D[k.sub.x, k.sub.y, k.sub.z +1] are employed instead of EQU (S[k.sub.x, k.sub.y, k.sub.z ]-O[k.sub.x, k.sub.y, k.sub.z ]), EQU (S[k.sub.x 1, k.sub.y, k.sub.z ]-O[k.sub.x -1, k.sub.y, k.sub.z ]), EQU (S[k.sub.x +1, k.sub.y, k.sub.z ]-O[k.sub.x +1, k.sub.y, k.sub.z ]), EQU (S[k.sub.x, k.sub.y -1, k.sub.z ]-O[k.sub.x, k.sub.y -1, k.sub.z ]), EQU (S[k.sub.x, k.sub.y +1, k.sub.z ]-O[k.sub.x, k.sub.y +1, k.sub.z ]), EQU (S[k.sub.x, k.sub.y, k.sub.z -1]-O[k.sub.x, k.sub.y, k.sub.z -1]), EQU (S[k.sub.x, k.sub.y, k.sub.z +1]-O[k.sub.x, k.sub.y, k.sub.z +1]), PA1 in the formula: ##EQU24## PA1 (1) predetermining constants .alpha..sub.ij each of which represents a physical field generated at a predetermined position by a physical source and having a unit quantity corresponding to the individual physical source, PA1 (2) provisionally estimating a physical quantity u.sub.i for each physical source, PA1 (3) calculating a physical quantity O.sub.j which is anticipated at the measurement point j by carrying out the operation of the equation: ##EQU26## (4) calculating a difference S.sub.j -O.sub.j between an actual measurement value S.sub.j at the measurement point j and the physical quantity O.sub.j. PA1 (5) obtaining a physical quantity u.sub.i as a provisional solution by carrying out operation of the quotation: ##EQU27## (6) carrying out steps (3) to (5) for each physical source, (7) iteratively repeating steps (3) to (5) until the sum of the squares of the differences S.sub.j -O.sub.j becomes less than a predetermined threshold value, and employing the physical quantity of each physical source which is finally obtained as analysis result. Determination of the estimation gains is not necessary and the speed of solution convergence can be increased because the estimation gains are disregarded. Further, an extent of applicable physical quantities is enlarged, and analysis with high stability and high accuracy is achieved. PA1 (1) predetermining constants .alpha..sub.ij each of which represents a unit quantity corresponding to the magnetic field generated at predetermined positions by a magnetic field source, PA1 (2) provisionally estimating a physical quantity u.sub.i for each magnetic field source positioned at a lattice point k (k=1, 2, . . . , p) within the object, PA1 (3) calculating a magnetic field O.sub.j which is anticipated at the measurement point j by carrying out the operation of the equation: ##EQU28## (4) calculating a difference S.sub.j -O.sub.j between an actual measurement value S.sub.j of magnetic field at the measurement point j and the magnetic field O.sub.j, PA1 (5) obtaining a physical quantity u.sub.i as a provisional solution by carrying out operation of the equation ##EQU29## (6) performing steps (3) to (5) for each magnetic field source, (7) iteratively repeating processing steps (3) to (5) until a sum of the squares of the differences S.sub.j -O.sub.j is less than a predetermined threshold value. Determination of the estimation gains is not necessary and the speed of solution convergence can be increased because the estimation gains are disregarded. That is, analysis of a magnetic source can be performed at high speed. PA1 (1) obtaining (N.sub.x -1).times.N.sub.y .times.N.sub.z number of G.sub.x [k.sub.x, k.sub.y, k.sub.z ], PA1 (2) obtaining N.sub.x .times.(N.sub.y -1).times.N.sub.z number of G.sub.y [k.sub.x, k.sub.y, k.sub.z ], PA1 (3) obtaining N.sub.x .times.N.sub.y .times.(N.sub.z -1) number of G.sub.z [k.sub.x, k.sub.y, k.sub.z ], PA1 (4) obtaining N.sub.x .times.N.sub.y .times.N.sub.z number of G.sub.N [k.sub.x, k.sub.y, k.sub.z ], PA1 (5) obtaining N.sub.x .times.N.sub.y .times.N.sub.z number of .beta.[k.sub.x, k.sub.y, k.sub.z ] based upon the equation: ##EQU33## (6) calculating correction values .DELTA.u of the potentials u[k.sub.x, k.sub.y, k.sub.z ] based upon the formula: ##EQU34## (7) correcting the potential u[k.sub.x, k.sub.y, k.sub.z ] by adding the calculated correction value .DELTA.u, PA1 (8) repeating the processing of steps (6) and (7) from 1 to N.sub.z for k.sub.z, PA1 (9) repeating the processing of steps (6) to (8) from 1 N.sub.y for k.sub.y, PA1 (10) repeating the processing of steps (6) to (9) from 1 to N.sub.x for k.sub.x, and PA1 (11) repeating the processing of steps (6) to (10) until an estimated error becomes smaller than a predetermined threshold value, PA1 (1) provisionally determining a current which flows into one lattice point and flows out from another lattice point of a physical source region subject to analysis, PA1 (2) calculating an estimated value of a potential on a surface of the region by multiplying the provisionally determined physical quantity and the proportion constant, PA1 (3) calculating a correction value for a physical quantity based upon a difference between the measured potential and the estimated value of the potential, PA1 (4) correcting the physical quantity based upon the calculated correction value, PA1 (5) repeating the processing of steps (2) to (4) for each physical quantity, then PA1 (6) repeating the processing of steps (2) to (5) until an estimated error becomes smaller than a predetermined threshold value. PA1 (1) selects two physical quantities from among a plurality of physical quantities, PA1 (2) calculates a correction value for each physical quantity based upon the formula: ##EQU35## (3) corrects corresponding physical quantities based upon each calculated correction value, PA1 (4) corrects a first physical quantity by carrying out the processing of steps (2) and (3), PA1 (5) corrects a second physical quantity by carrying out the processing of steps (2) and (3), PA1 (6) corrects the first physical quantity again by carrying out the processing of steps (2) and (3), PA1 (7) calculates a correction value for correcting the second physical quantity again, by carrying out the processing of step (2), PA1 (8) calculates a correction value for the first physical quantity by dividing a product of the correction values which are obtained in steps (6) and (7) by a difference between the correction value obtained in the step (4) and the correction value obtained in the step (6), PA1 (9) calculates a correction value for the second physical quantity by dividing a product of the correction values which are obtained in steps (5) and (7) by a difference between the correction value obtained in the step (4) and the correction value obtained in the step (6), PA1 (10) corrects the physical quantities based upon one of the correction values obtained in steps (8) and (9), PA1 (11) selects two other physical quantities and carries out the processing of steps (4) to (10), then PA1 (12) repeats the processing of steps (4) to (11) until an estimated error becomes smaller than a predetermined threshold value. PA1 calculating the estimated errors of EQU D[k.sub.x, k.sub.y, k.sub.z ]=(S[k.sub.x, k.sub.y, k.sub.z ]-O[k.sub.x, k.sub.y, k.sub.z ]), EQU D[k.sub.x -1, k.sub.y, k.sub.z ]=(S[k.sub.x -1, k.sub.y, k.sub.z ]-O[k.sub.x -1, k.sub.y, k.sub.z ]), EQU D[k.sub.x +1, k.sub.y, k.sub.z ]=(S[k.sub.x +1, k.sub.y, k.sub.z ]-O[k.sub.x +1, k.sub.y, k.sub.z ]), EQU D[k.sub.x, k.sub.y -1, k.sub.z ]=(S[k.sub.x, k.sub.y -1, k.sub.z ]-O[k.sub.x, k.sub.y -1, k.sub.z ]), EQU D[k.sub.x, k.sub.y +1, k.sub.z ]=(S[k.sub.x, k.sub.y +1, k.sub.z ]-O[k.sub.x, k.sub.y +1, k.sub.z ]), EQU D[k.sub.x, k.sub.y, k.sub.z -1]=(S[k.sub.x, k.sub.y, k.sub.z -1]-O[k.sub.x, k.sub.y, k.sub.z -1]), EQU D[k.sub.x, k.sub.y, k.sub.z +1]-(S[k.sub.x, k.sub.y, k.sub.z +1]-O[k.sub.x, k.sub.y, k.sub.z +1]) PA1 and PA1 correcting the estimated errors based upon the formulae: EQU D[k.sub.x, k.sub.y, k.sub.z ].rarw.(D[k.sub.x, k.sub.y, k.sub.z ]+G.sub.N [k.sub.x, k.sub.y, k.sub.z ]).DELTA.u EQU D[k.sub.x -1, k.sub.y, k.sub.z ].rarw.(D[k.sub.x -1, k.sub.y, k.sub.z ]+G.sub.x [k.sub.x -1, k.sub.y, k.sub.z ]).DELTA.u EQU D[k.sub.x +1, k.sub.y, k.sub.z ].rarw.(D[k.sub.x +1, k.sub.y, k.sub.z ]+G.sub.x [k.sub.x, k.sub.y, k.sub.z ]).DELTA.u EQU D[k.sub.x, k.sub.y -1, k.sub.z ].rarw.(D[k.sub.x, k.sub.y -1, k.sub.z ]+G.sub.y [k.sub.x, k.sub.y -1, k.sub.z ]).DELTA.u EQU D[k.sub.x, k.sub.y +1, k.sub.z ].rarw.(D[k.sub.x, k.sub.y +1, k.sub.z ]+G.sub.y [k.sub.x, k.sub.y, k.sub.z ]).DELTA.u EQU D[k.sub.x, k.sub.y, k.sub.z -1].rarw.(D[k.sub.x, k.sub.y, k.sub.z -1]+G.sub.z [k.sub.x, k.sub.y, k.sub.z -1]).DELTA.u EQU D[k.sub.x, k.sub.y, k.sub.z +1].rarw.(D[k.sub.x, k.sub.y, k.sub.z +1]+G.sub.z [k.sub.x, k.sub.y, k.sub.z ]).DELTA.u (9) PA1 wherein D[k.sub.x, k.sub.y, k.sub.z ], D[k.sub.x -1, k.sub.y, k.sub.z ], D[k.sub.x +1, k.sub.y, k.sub.z ], D[k.sub.x, k.sub.y -1, k.sub.z ], D[k.sub.x, k.sub.y +1, k.sub.z ], D[k.sub.x, k.sub.y, k.sub.z -1], D[k.sub.x, k.sub.y, k.sub.z +1] are employed instead of EQU (S[k.sub.x, k.sub.y, k.sub.z ]-O[k.sub.x, k.sub.y, k.sub.z ]), EQU (S[k.sub.x -1, k.sub.y, k.sub.z ]-O[k.sub.x -1, k.sub.y, k.sub.z ]), EQU (S[k.sub.x +1, k.sub.y, k.sub.z ]-O[k.sub.x +1, k.sub.y, k.sub.z ]), EQU (S[k.sub.x, k.sub.y -1, k.sub.z ]-O[k.sub.x, k.sub.y -1, k.sub.z ]), EQU (S[k.sub.x, k.sub.y +1, k.sub.z ]-O[k.sub.x, k.sub.y +1, k.sub.z ]), EQU (S[k.sub.x, k.sub.y, k.sub.z -1]-O[k.sub.x, k.sub.y, k.sub.z -1]), EQU (S[k.sub.x, k.sub.y, k.sub.z +1]-O[k.sub.x, k.sub.y, k.sub.z +1]) PA1 in the formula: ##EQU36## PA1 predetermines constants .alpha..sub.ij each of which represents a physical field measurable at each predetermined position which is generated by a physical source and which physical source has a unit quantity corresponding to the individual physical source by the means (1) for predetermining constants, PA1 provisionally determines a physical quantity u.sub.i corresponding to each physical source by the means (2) for provisionally determining physical quantity, PA1 calculates a physical quantity O.sub.j which is predicted at the measurement point j by carrying out the operation of the equation: ##EQU38## by the means (3) for calculating physical quantity, calculates a difference S.sub.j -O.sub.j between an actual measurement value S.sub.j at the measurement point j and the physical quantity O.sub.j by the means (4) for calculating difference, PA1 obtains a physical quantity u.sub.i as a provisional solution by carrying out operation of the equation ##EQU39## by the means (5) for obtaining physical quantity, carries out the processing of each of the means (3) to (5) for each physical source i by the means (6) for carrying out the operation of the means (3) to (5), PA1 iteratively repeats processing of each of the means (3) to (5) until the sum of the squares of the differences S.sub.j -O.sub.j is less than a predetermined threshold value by the means (7) for continuing the repeating operation of the processing of each of the means (3) to (5), and PA1 employs the physical quantity u.sub.i of each physical source which is finally obtained by the means (8) for employing physical quantity. PA1 predetermines constants .alpha..sub.ij each of which represents a magnetic field, which is generated at each predetermined position by a magnetic field source having a unit quantity corresponding to the individual magnetic field source by the means (1) for predetermining constants, PA1 provisionally determine a physical quantity u.sub.i for each magnetic field source corresponding to a lattice point k (k=1, 2, . . . , p) within the object by the means (2) for provisionally determining physical quantity, PA1 calculates a magnetic field O.sub.j which is anticipated at the measurement point j by carrying out the operation of the equation ##EQU40## by the means (3) for calculating magnetic field, calculates a difference S.sub.j -O.sub.j between an actual measurement value S.sub.j of magnetic field at the measurement point j and the magnetic field O.sub.j determined by the means (4) for calculating difference, PA1 obtains a physical quantity u.sub.i as a provisional solution by carrying out operation of the equation: ##EQU41## by the means (5) for obtaining physical quantity, carries out the processing by each of the means (3) to (5) for each magnetic field source by the means (6) for carrying out the processing by each of the means (3) to (5), PA1 iteratively repeats processing of each of the means (3) to (5) until the sum of the squares of the differences S.sub.j -O.sub.j is less than a predetermined threshold value by the means (7) for repeating the processing by each of the means (3) to (5), and PA1 employs the physical quantity u.sub.i which is finally obtained as the physical quantity u.sub.i corresponding to each physical source which is finally obtained as analysis result by the means (8) for employing physical quantity. PA1 pre-obtaining and holding the proportion consteants which are determined based upon the region by using a proportion constant holding means, PA1 provisionally determining physical quantities at a plurality of predetermined positions by a provisional physical quantity determining means, PA1 calculating a difference between a known physical quantity corresponding to a predetermined position within the region and a sum of products of each physical quantity and corresponding proportion constant by using a difference calculating means, PA1 employing a value which minimizes the sum of squares of differences as a new physical quantity based upon the calculated differences and each physical quantity measurement value of each active physical source by using a physical quantity renewing means, PA1 repeating the calculating of the difference by the difference calculating means and the employing of the physical quantities by the physical quantity renewing means for each physical source by a first repetition controlling means, and PA1 iterating the repetition of the calculating of the difference by the difference calculating means and employing of the physical quantities for each physical source until the sum of the squares of the differences which is obtained by the repetition of the processing becomes smaller than a predetermined threshold value, and then employing the physical quantity which is finally obtained as physical quantity for the predetermined position by a physical quantity employment means. PA1 obtains (N.sub.x -1).times.N.sub.y .times.N.sub.z number of G.sub.x [k.sub.x, k.sub.y, k.sub.z ] by the means (1) for obtaining (N.sub.x -1).times.N.sub.y .times.N.sub.z number of G.sub.x [k.sub.x, k.sub.y, k.sub.z ], PA1 obtains N.sub.x .times.(N.sub.y -1).times.N.sub.z number of G.sub.y [k.sub.x, k.sub.y, k.sub.z ] by the means (2) for obtaining N.sub.x .times.(N.sub.y -1).times.N.sub.z number of G.sub.y [k.sub.x, k.sub.y, k.sub.z ], PA1 obtains N.sub.x .times.N.sub.y .times.(N.sub.z -1) number of G.sub.z [k.sub.x, k.sub.y, k.sub.z ] by the means (3) for obtaining N.sub.x .times.N.sub.y .times.(N.sub.z -1) number of G.sub.z [k.sub.x, k.sub.y, k.sub.z ], PA1 obtains N.sub.x .times.N.sub.y .times.N.sub.z number of G.sub.N [k.sub.x, k.sub.y, k.sub.z ] by the means (4) for obtaining N.sub.x .times.N.sub.y .times.N.sub.z number of G.sub.N [k.sub.x, k.sub.y, k.sub.z ], PA1 obtains N.sub.x .times.N.sub.y .times.N.sub.z number of .beta.[k.sub.x, k.sub.y, k.sub.z ] based upon the equation ##EQU45## by the means (5) for obtaining N.sub.x .times.N.sub.y .times.N.sub.z number of .beta.[k.sub.x, k.sub.y, k.sub.z ], PA1 calculates correction values .DELTA.u of the potentials u[k.sub.x, k.sub.y, k.sub.z ] based upon the formula ##EQU46## by the means (6) for calculating correction values, corrects the potential u[k.sub.x, k.sub.y, k.sub.z ] by adding the calculated correction value .DELTA.u by the means (7) for correcting potentials, PA1 repeats the process for each of the means (5) and (7) from 1 to N.sub.z for k.sub.z by the means (8) for repeating process of the means (6) and (7), PA1 repeats the process for each of the means (6) to (8) from 1 to N.sub.y for k.sub.y by the means (9) for repeating process of the means (6) to (8), PA1 repeats the process for each of the means (6) to (9) from 1 to N.sub.x for k.sub.x by the means (10) for repeating process of the means (6) to (9), and PA1 repeats the process for each of the means (6) to (10) until an estimated error becomes smaller than a predetermined threshold value, and employs the potentials which are finally obtained as an analysis result by the means (11) for repeating process of the means (6) to (10). PA1 provisionally determining a current which flows into one lattice point and flows out from another lattice point of a physical source which is the subject of analysis by the means (1) for provisionally determining current flowing into and current flowing out, PA1 calculating an estimated value of a potential on a surface of the region subject to analysis by multiplying the provisionally determined physical quantity and the proportion constant by the means (2) for calculating estimated value of potential, PA1 calculating a correction value for one physical quantity based upon a difference between the measured potential and the estimated value of the potential by the means (3) for calculating correction value, PA1 correcting the one physical quantity based upon the calculated correction value by the means (4) for correcting the one physical quantity, PA1 repetitively operating each of the means (2) to (4) for all physical quantities by the means (5) for repetitively operating each of the means (2) to (4), and PA1 repetitively operating each of the means (2) to (5) until an estimated error becomes smaller than a predetermined threshold value by the means (6) for iteratively operating each of the means (2) to (5). The final results are employed by the means for employing physical quantities. PA1 selects two physical quantities from among a plurality of physical quantities by the means (1) for selecting two physical quantities, PA1 calculates a correction value for each physical quantity based upon the formula ##EQU47## by the means (2) for calculating a correction value, corrects corresponding physical quantities based upon each calculated correction value by the means (3) for correcting a corresponding physical quantity, PA1 corrects a first physical quantity by operating each of the means (2) and (3) by the means (4) for correcting a first physical quantity, PA1 corrects a second physical quantity by operating each of the means (2) and (3) by the means (5) for correcting a second physical quantity, PA1 corrects the first physical quantity again by operating each of the means (2) and (3) by the means (6) for correcting a first physical quantity again, PA1 calculates a correction value for correcting the second physical quantity again, by operating the means (2) by the means (7) for correcting a second physical quantity again, PA1 calculates a correction value by the means (8) for calculating a correction value for the first physical quantity for the first physical quantity by dividing a product of the correction values which are obtained by operating each of the means (6) and (7) by a difference between the correction value which is obtained by operating the means (4) and the correction value obtained by operating the means (6), PA1 calculates a correction value by the means (9) for calculating a correction value for the second physical quantity for the second physical quantity by dividing a product of the correction values which are obtained by operating each of the means (5) and (7) by a difference between the correction value which is obtained by operating the means (4) and the correction value which is obtained by operating the means (6), PA1 corrects the physical quantities based upon one of the correction values which are obtained by operating each of the means (8) and (9) by the means (10) for correcting the physical quantities, PA1 selects other two physical quantities and for operating each of the means (4) to (10) by the means (11) for selecting other two physical quantities, and PA1 repetitively operates each of the means (4) to (11) until an estimated error becomes smaller than a predetermined threshold value, and employs the physical quantities which are obtained as the analysis result by the means (12) for iteratively operating each of means (4) to (11). PA1 means for calculating the estimated errors of EQU D[k.sub.x, k.sub.y, k.sub.z ]=(S[k.sub.x, k.sub.y, k.sub.z ]-O[k.sub.x, k.sub.y, k.sub.z ]), EQU D[k.sub.x -1, k.sub.y, k.sub.z ]=(S[k.sub.x -1, k.sub.y, k.sub.z ]-O[k.sub.x -1, k.sub.y, k.sub.z ]), EQU D[k.sub.x 1, k.sub.y, k.sub.z ]=(S[k.sub.x +1, k.sub.y, k.sub.z ]=O[k.sub.x +1, k.sub.y, k.sub.z ]), EQU D[k.sub.x, k.sub.y -1, k.sub.z ]=(S[k.sub.x, k.sub.y -1, k.sub.z ]-O[k.sub.x, k.sub.y i, k.sub.z ]) EQU D[k.sub.x, k.sub.y +1, k.sub.z ]=(S[k.sub.x, k.sub.y +1, k.sub.z ]-O[k.sub.x, k.sub.y +1, k.sub.z ]), EQU D[k.sub.x, k.sub.y, k.sub.z -1]=(S[k.sub.x, k.sub.y, k.sub.z -1-O[k.sub.x, k.sub.y, k.sub.z -1]) EQU D[k.sub.x, k.sub.y, k.sub.z +1]=(S[k.sub.x, k.sub.y, k.sub.z +1]-O[k.sub.x, k.sub.y, k.sub.z +1]) PA1 and PA1 means for correcting the estimated errors based upon the formulae EQU D[k.sub.x, k.sub.y, k.sub.z ].rarw.(D[k.sub.x, k.sub.y, k.sub.z ]+G.sub.N [k.sub.x, k.sub.y, k.sub.z ]).DELTA.u EQU D[k.sub.x -1, k.sub.y, k.sub.z ].rarw.(D[k.sub.x -1, k.sub.y, k.sub.z ]+G.sub.x [k.sub.x -1, k.sub.y k.sub.z ]).DELTA.u EQU D[k.sub.x +1, k.sub.y, k.sub.z ].rarw.(D[k.sub.x +1, k.sub.y, k.sub.z ]+G.sub.x [k.sub.x, k.sub.y, k.sub.z ]).DELTA.u EQU D[k.sub.x, k.sub.y -1, k.sub.z ].rarw.(D[k.sub.x, k.sub.y -1, k.sub.z ]+G.sub.y [k.sub.x, k.sub.y -1, k.sub.z ]).DELTA.u EQU D[k.sub.x, k.sub.y +1, k.sub.z ].rarw.(D[k.sub.x, k.sub.y +1, k.sub.z ]+G.sub.y [k.sub.x, k.sub.y, k.sub.z ]).DELTA.u EQU D[k.sub.x, k.sub.y, k.sub.z -1].rarw.(D[k.sub.x, k.sub.y, k.sub.z -1]+G.sub.z [k.sub.x, k.sub.y, k.sub.z -1]).DELTA.u EQU D[k.sub.x, k.sub.y, k.sub.z +1].rarw.(D[k.sub.x, k.sub.y, k.sub.z +1]+G.sub.z [k.sub.x, k.sub.y, k.sub.z ]).DELTA.u (9), PA1 wherein D[k.sub.x, k.sub.y, k.sub.z ], D[k.sub.z -1, k.sub.y, k.sub.z ], D[k.sub.x +1, k.sub.y, k.sub.z ], D[k.sub.x, k.sub.y -1, k.sub.z ], D[k.sub.x, k.sub.y +1, k.sub.z ], D[k.sub.x, k.sub.y, k.sub.z -1], D[k.sub.x, k.sub.y, k.sub.z +1] are employed instead of EQU (S[k.sub.x, k.sub.y, k.sub.z ]-O[k.sub.x, k.sub.y, k.sub.z ]), EQU (S[k.sub.x -1, k.sub.y, k.sub.z ]-O[k.sub.x -1, k.sub.y, k.sub.z ]), EQU (S[k.sub.x +1, k.sub.y, k.sub.z ]-O[k.sub.x +1, k.sub.y, k.sub.z ]), EQU (S[k.sub.x, k.sub.y -1, k.sub.z ]-O[k.sub.x, k.sub.y -1, k.sub.z ]), EQU (S[k.sub.x, k.sub.y +1, k.sub.z ]-O[k.sub.x, k.sub.y +1, k.sub.z ]), EQU (S[k.sub.x, k.sub.y, k.sub.z -1]-O[k.sub.x, k.sub.y, k.sub.z -1]), EQU (S[k.sub.x, k.sub.y, k.sub.z +1]-O[k.sub.x, k.sub.y, k.sub.z +1]), PA1 in the formula ##EQU48## and it is sufficient that D[k.sub.x, k.sub.y, k.sub.z ], D[k.sub.x -1, k.sub.y, k.sub.z ], D[k.sub.x +1, k.sub.y, k.sub.z ], D[k.sub.x, k.sub.y -1, k.sub.z ], D[k.sub.x, k.sub.y +1, k.sub.z ], D[k.sub.x, k.sub.y, k.sub.z -1], D[k.sub.x, k.sub.y, k.sub.z +1] are held in a memory instead of holding S[k.sub.x, k.sub.y, k.sub.z ], S[k.sub.x -1, k.sub.y, k.sub.z ], S[k.sub.x +1, k.sub.y, k.sub.z ], S[k.sub.x, k.sub.y -1, k.sub.z ], S[k.sub.x, k.sub.y +1, k.sub.z ], S[k.sub.x, k.sub.y, k.sub.z -1], S[k.sub.x, k.sub.y, k.sub.z +1] and O[k.sub.x, k.sub.y, k.sub.z ], O[k.sub.x -1, k.sub.y, k.sub.z ], O[k.sub.x +1, k.sub.y, k.sub.z ], O[k.sub.x, k.sub.y -1, k.sub.z ], O[k.sub.x, k.sub.y +1, k.sub.z ], O[k.sub.x, k.sub.y, k.sub.z -1], O[k.sub.x, k.sub.y, k.sub.z +1] so that PA1 memory capacity can be decreased. In the repeat processing operations of EQU (S[k.sub.x, k.sub.y, k.sub.z ]-O[k.sub.x, k.sub.y, k.sub.z ]), EQU (S[k.sub.x -1, k.sub.y, k.sub.z ]-O[k.sub.x -1, k.sub.y, k.sub.z ]), EQU (S[k.sub.x +1, k.sub.y, k.sub.z ]-O[k.sub.x +1, k.sub.y, k.sub.z ]), EQU (S[k.sub.x, k.sub.y -1, k.sub.z ]-O[k.sub.x, k.sub.y -1, k.sub.z ]), EQU (S[k.sub.x, k.sub.y +1, k.sub.z ]-O[k.sub.x, k.sub.y +1, k.sub.z ]), EQU (S[k.sub.x, k.sub.y, k.sub.z -1]-O[k.sub.x, k.sub.y, k.sub.z -1]), EQU (S[k.sub.x, k.sub.y, k.sub.z +1]-O[k.sub.x, k.sub.y, k.sub.z +1]) PA1 are not necessarily performed, but the estimated errors are easily corrected using the calculated correction values so that operations are simplified and the time required for correcting estimated errors is shortened.
An adaptive noise canceler incorporating the method is illustrated in FIG. 27 and operates as follows. An input S.sub.j which is made by mixing a noise from a noise source 72 to information from a signal source 71 is supplied to a non-inversed input terminal of an error computing element 73. Only the noise from the noise source 72 is supplied to an inversed input terminal of the error computing element 73 through an FIR filter 74. An output from the error computing element 73 is feedbacked to the FIR filter 74. The FIR filter 74 employs a LMS (Least Mean Square) algorithm.
The adaptive noise canceler can remove only noise in information by determining an estimation gain to be a proper value. Therefore, noise of a duct of an air conditioner can be eliminated, and the passenger area of an automobile can be made to be quiet and so on. That is, noise which should be removed are accurately estimated.
An impulse response estimating apparatus incorporating the method performs analysis of frequency components using a fast Fourier transform (hereinafter referred to as FFT) and estimates an impulse response based upon the analysis result.
A method for solving threshold values, coupling coefficients, and the like, for neural systems has already been filed in a patent application by the applicant of this patent application, and is illustrated in FIG. 28. An input pattern is supplied to plural physical formula operating units 811, 812, . . . , 81m so as to operate based upon a known physical formula. Outputs from all physical formula operating units 811, 812, . . . , 81m are supplied to a sigma unit 82 so as to obtain a sum. The sum and an actual measurement value are supplied to an error operating device 83 so as to obtain an error (a difference between the estimated and actual values). The obtained error is fed back to correction sections 811a, 812a, . . . , 81ma of the physical formula operating units 811, 812, . . . , 81m. Values of variables which are estimated in the physical formula operating units 811, 812, . . . , 81m are collected and outputted as analysis results by an information collection unit 84.
Therefore, no physical formula operating units are required learning of a physical formula. The analysis result with high accuracy is obtained by repeating the correction based upon the error and estimation gains for only the variables which are included in the physical formula.
The method for finite element analysis which is widely utilized in variable field such as structure analysis in architecture and machinery, weather calculation, calculating astronomy, electromagnetic analysis and the like. The method constructs a model by dividing an object for analysis into finite number of elements. The method then solves simultaneous linear equations which are given based upon the model so as to obtain a physical source analysis result. Various methods such as Gauss' erasing method, SOR method, CD method, SD method and the like are known as methods for solving simultaneous linear equations.
Method for analyzing magnetic field sources varies parameters of the current element k by extremely small quantities so as to minimize total estimated error, until a correct analysis result is finally obtained. But, it is not guaranteed that the total estimated error will become smaller when the processing is carried out once. Disadvantages arise in that a remarkably long time period is required even when a super computer is employed and that a final solution cannot be obtained even when the number of times of the processings is increased, because only part of the processing can typically be processed in parallel and the other parts of the processing (e.g., the processing for operating a magnetic field which is made up by m-numbered current elements, and the processing for obtaining a total estimated error) can not be processed in parallel.
The adaptive noise canceler requires determination of an estimation gain because the adaptive noise canceler employs a LMS algorithm. A disadvantage arises in that it is difficult to determine a proper estimation gain. More particularly, a number of propagation paths of the noise is extremely great. The noise from the noise source 72 could be delayed by an extremely short time and proper estimation gains should be determined for all delayed noises for accurately estimating actual noise which reaches a position selected for noise cancelling through all propagation paths. As a result, the number of estimation gains which should be determined becomes extremely large, and all the estimation gains should be properly determined. If all estimation gains are determined to be the same value, all the estimation gains are inevitably determined to be a small value so that no estimation processing diverges. Convergence of solutions becomes slow following the estimation gains becoming small.
The impulse estimating response method suffers the following disadvantages because the method employs FFT. Though FFTs is a method for performing processing based upon a sampling theorem, it is necessary that a low pass filter, called an antialiasing filter, be provided for omitting unwanted higher harmonics which are usually included in a measurement signal, which results in a complicated arrangement. Accuracy of frequency analysis result is extremely low when data in a sampling interval is not periodic. To solve these disadvantages, it is proposed that a window function such as hamming, hunning, or the like, be utilized. When the window function is used in a reverse filtering operation, a new disadvantage arises in that a waveform is deformed in the sampling interval after the operation so that analysis accuracy is lowered. Further, another disadvantage arises in that a number of samples should be increased when analysis for a wide band is necessary, because only outputs at frequency intervals determined based upon sampling intervals are obtained. A further disadvantage arises in that an extremely large quantity of memory is necessary because sampling should be performed by constant intervals even when a frequency axis has a logarithmic scale and a number of samples is limited to 2.sup.N.
The method in neural systems performs correction processing using a value which is obtained by multiplying an estimation gain to a sum of products of partial differential values of physical formula operation results and errors, consequently estimation gains are necessary. A number of estimation gains which should be determined is increased when a proper number of estimation gains is determined, resulting in the determination of estimation gains becoming extremely complicated. If, all estimation gains are determined to be the same value for simplicity, then all estimation gains are inevitably determined to be a small value so that estimation processing does not diverge. Convergence of solutions becomes slow following the estimation gains becoming small.
The method applied to finite element analysis can improve analysis accuracy of physical quantities by increasing a mesh division number.
However, when Gauss' erasing method is employed for solving simultaneous linear equations, and it is assumed that a number of unknowns is n, operation frequency on an order of n.sup.3 /3 is necessary so that operation load becomes unwieldy. Therefore, when a number of unknowns is great, physical source analyzing with succient speed cannot be practically performed even when a super computer is employed. When Choleski's method is employed, operation frequency can be made on an order of n.sup.3 /6, but operation load is too great for a method for solving simultaneous linear equations having a large size. In both methods, errors are cumulative so that physical source analyzing accuracy cannot be significantly improved.
The SOR method is a method for performing excessive correction by introducing acceleration parameters so as to accelerate convergence of Gauss-Seidel's method. Therefore, convergence of solutions is guaranteed for a coefficient matrix which satisfies a predetermined condition, but convergence of solutions is not guaranteed for a coefficient matrix which does not satisfy the predetermined condition. There is not a method for securely and easily obtaining proper values of the acceleration parameters even when the coefficient matrix is guaranteed convergence of solution. When determined acceleration parameters are not proper, the convergence of solution is insufficiently accelerated.
The SD method is a method which is also called a maximum grade direction decreasing method. This method does not have the limit in a coefficient matrix of the SOR method. The SD method involves an extreme increase in repetition, it also requires a calculation of a maximum grade direction, a calculation of gain for correcting unknowns is carried out for each repetition cycle. In addition these calculations include vector operations and subtractions. Therefore operation load, as a whole, is extreme.
The CG method is also called a conjugate gradient method. This method determines a direction as a correction direction which is vertical to all directions in which direction corrections have already been made, and corrects unknowns sequentially. Therefore, repetition is dramatically decreased in theory (the repetition number of times can be made to be less than n). In theory, physical source analysis accuracy also is increased. However, in actual use, errors are typically generated in correction processing, therefore, the repetition number greatly varies depending upon matrix coefficients. Further, vector operations and subtractions are necessary for performing each repetition. Therefore operation load increases.